Determine the output of a linear time-invariant system if the impulse response h[n] and the input x[n] are as follows:

(a) x[n] = u[n] and h[n] = aⁿu[–n – 1], with α > 1.

(b) x[n] = u[n – 4] and h[n] = 2ⁿu[–n–1].

(c) x[n] = u[n] and h[n] = (0.5)2ⁿu[–n].

(d) h[n] = 2ⁿu[–n –1] and x[n] = u[n] – u[n – 10]  

Use your knowledge of linearity and time invariance to minimize the work in parts (b)–(d).